Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

If you thought that learning Newton's Laws of Motions was only useful to pass a physics test, think again! In this lesson, we'll learn how to use them to calculate mass and weight, two related but different concepts.

Review of Newton's Laws

Before we put Newton's Laws of Motion to use, let's make sure that we remember what they are. Newton's First Law is the idea of inertia, or that a body in motion stays in motion while an object at rest stays at rest. Newton's Second Law is the idea that force is equal to mass times acceleration. Finally, Newton's Third Law states that for every action there is an equal and opposite reaction.

So what do all these laws have to do with finding mass and weight? Everything. However, of the three laws of motion, by far, the most useful for our purposes is the second law. That said, keep those other two fresh in your head as well, as we may refer back to them to justify any statements we make.

What Is Mass?

Let's say that I have a car with a mass of 1,000 kilograms. What does that even mean? Couldn't I just say that the car weighs 1,000 kilograms? Actually, no. Mass is a measure of how much matter is present in an object. By saying that my car has a mass of 1,000 kilograms, I am saying that no matter where I take that car, there will always be the same amount of mass there. The only ways that I can change the mass of that car would be to put a custom body kit on it, adding to the mass, or taking a sledgehammer to the thing, reducing the mass.

Solving for Mass

Newton's Second Law of Motion makes it possible for us to solve for mass if we know the acceleration and force of the object. Remember, force is equal to mass times acceleration. Therefore, if we divide the force by acceleration, the resulting answer should give us the mass of the object in question. Let's give it a shot. Let's say that my car has a force of 9800 newtons (N), the unit used to measure force, on the ground. Remember that acceleration due to gravity is 9.8 meters per second squared. We know that it is having a force on the ground due to Newton's Third Law, the one about equal and opposite reactions, right?

So let's solve the math. 9800 newtons divided by 9.8 meters per second squared leaves 1000 kilograms. Remember that a newton is equal to a kilogram meter per second squared. See, it's just shorter to call them 'newtons.'

What Is Weight?

So what is weight, then? Simply put, weight is the force that we have due to gravity. This is why people can be weightless in space; they are subject to reduced amounts of gravity. On the Moon, someone weighs 1/6 of what they weigh on the Earth due to the fact that the gravity on the Moon is only 1/6 of the total on Earth.

In fact, we can take this even further. Let's say you were on Mount Everest, the tallest mountain in the world. Likewise, your identical twin was standing on the shores of the Dead Sea, the lowest land on the planet. At sea level, you both weigh the same. However, due to the pull of gravity being stronger at the Dead Sea than it is on Mount Everest, your twin weighs more than you do. Importantly, you still have the same mass.

Solving for Weight

Since weight is simply a matter of force, we just have to plug the relevant numbers into the formula to find out how much the weight difference is for you and your twin. Let's say you both have a mass of 75 kilograms and for the purposes of this experiment, acceleration due to gravity at Mount Everest is 9.7 meters per second squared, while it is 9.9 meters per second squared at the Dead Sea. (These values are slightly exaggerated, but I think you'd prefer a slight exaggeration than more decimals.) At the Dead Sea, your twin has a force of 742.5 newtons. Meanwhile, on the top of Mount Everest, your force is 727.5 newtons. In short, you weigh 15 newtons less. That comes out to about 3 pounds.

Lesson Summary

In this lesson, we used Newton's Laws of Motion, specifically, the Second Law of Motion, to solve for mass and weight. Remember that mass is a measure of the amount of matter present in an object, while weight is a measure of the force of gravity on an object. This means that we can solve force (or weight) as equal to mass times acceleration for weight, while mass is equal to force divided by acceleration.

Newton's Three Laws

Newton's First Law is the idea that a body in motion stays in motion while an object at rest stays at rest.

Newton's Second Law is the idea that force is equal to mass times acceleration.

Newton's Third Law states that for every action there is an equal and opposite reaction.

Summary:

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